A (co)algebraic theory of succinct automata

Abstract

The classical subset construction for non-deterministic automata can be
generalized to other side-effects captured by a monad. The key insight is that
both the state space of the determinized automaton and its semantics—languages
over an alphabet—have a common algebraic structure: they are Eilenberg-Moore
algebras for the powersetgen monad. In this paper we study the reverse question
to determinization. We will present a construction to associate succinct
automata to languages based on different algebraic structures. For instance,
for classical regular languages the construction will transform a deterministic
automaton into a non-deterministic one, where the states represent the
join-irreducibles of the language accepted by a (potentially) larger
deterministic automaton. Other examples will yield alternating automata,
automata with symmetries, CABA-structured automata, and weighted automata.